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Adaptive hybrid High-Order terminal sliding mode control of MIMO uncertain nonlinear systems and its application to robot manipulators

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Abstract

This paper proposes an adaptive hybrid high-order terminal sliding mode (HHOTSM) control approach for a class of high-order multiple-input and multiple-output (MIMO) uncertain nonlinear systems and its application to robotic manipulators. The techniques of the terminal sliding mode (TSM) control and a type of traditional sliding mode control (SMC) are combined to establish the HHOTSM controller, in which the first-order sliding mode term is designed based on the TSM, while the high-order sliding mode term is defined based on the idea of the high-order sliding mode approach. Thus, the proposed method offers a valuable elimination of the singularity problem encountered in traditional TSM control, as well as the reaching phase problem. It is guaranteed that the tracking errors will converge to zero in some finite time that can be set arbitrarily, and the actual control input signal is smooth and free of chattering effects. Furthermore, an adaptive tuning law is incorporated to reject the effects of unknown system uncertainties. The convergence and stability of the proposed method are verified by the Lyapunov stability theory. Simulation results of a robot manipulator are presented to demonstrate the effectiveness and applicability of the proposed method.

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Abbreviations

SMC:

Sliding Mode Control

TSM:

Terminal Sliding Mode Control

VSS:

Variable Structure System

HOSMC:

High-Order Sliding Mode Control

HHOTSM:

Hybrid High-Order Terminal Sliding Mode

AHHOTSM:

Adaptive HHOTSM

SISO:

Single-Input and Single-Output

MIMO:

Multiple-Input and Multiple-Output

T c :

Convergence time

T f :

Total running time

N c :

Total sampling instant in interval time [Tc, Tf]

N f :

Total sampling instant in interval time [0, Tf]

MAET c :

Mean-Absolute-Error in interval time [Tc, Tf]

ITAE :

Integral of Time multiply Absolute Error

TV :

Total Variation

N2 :

Consumption of Energy

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  1. School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 680-749, South Korea

    Xuan-Toa Tran & Hee-Jun Kang

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Correspondence to Hee-Jun Kang.

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Tran, XT., Kang, HJ. Adaptive hybrid High-Order terminal sliding mode control of MIMO uncertain nonlinear systems and its application to robot manipulators. Int. J. Precis. Eng. Manuf. 16, 255–266 (2015). https://doi.org/10.1007/s12541-015-0034-0

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